exponents

[J N]

from veritas prep

if m and n are integers what is m+n?

36/(3^4) = 1/(3^m) + 1/(3^n)


-2
0
2
3
5

[srcc25anu]

36/81 = 4/9

4/9 = 1/9 + 3/9 or 4/9 = 1/9 + 1/3
Now 1/9 + 1/3 = 1/3^m + 1/3^n
so 3^m = 3 hence m = 1 (3^1 = 3)AND
so 3^n = 9 hence n = 2 (3^2 = 9)
therefore m + n = 1+2 = 3
Ans D

[GMATGuruNY]

from veritas prep

if m and n are integers what is m+n?

36/(3^4) = 1/(3^m) + 1/(3^n)


-2
0
2
3
5

Plug in m = 1 and solve for n:

36/3� = 1/3¹ + 1/(3^n)

36/81 = 1/3 + 1/(3^n)

4/9 = 1/3 + 1/(3^n)

1/9 = 1/(3^n).

Since 1/9 = 1/3², n = 2.
Thus, m+n = 1+2 = 3.

The correct answer is D.